JTAS Ferreira and MFJ Steel
Abstract: We introduce a general perspective on the introduction of skewness into symmetric distributions. Through inverse probability integral transformations we provide a constructive representation of skewed distributions, where the skewing mechanism and the original symmetric distributions are specified separately. We study the e®ects of the skewing mechanism on e.g. modality, tail behaviour and the amount of skewness generated. The representation is used to introduce novel classes of skewed distributions, where we induce certain prespecified characteristics through particular choices of the skewing mechanism. Finally, we use a Bayesian linear regression framework to compare the new classes with some existing distributions in the context of two empirical examples.
Keywords: Arnold and Groeneveld skewness measure, Bayesian regression model, inverse probability integral transformation, modality, skewing mechanism, tail behaviour